1. Field of the Invention
The present invention relates to an alignment method suitable for an exposure apparatus, a repairing apparatus and an inspecting apparatus which are employed in the process of manufacturing, e.g., a semiconductor device, a liquid crystal display device and a thin-film magnetic head.
2. Related Background Art
In the process of manufacturing a semiconductor device, etc., particularly in a photolithography process, there is employed a projection exposure apparatus (a stepper) for transferring a pattern on a mask or a reticle (hereinafter generically termed a reticle) onto a substrate (a semiconductor wafer, a glass plate or the like) coated with a photosensitive material (a photoresist) via a projection optical system. When projection-exposing the reticle pattern on a shot area on the wafer while being overlapped therewith, it is required that a projected image of the reticle pattern be aligned exactly with the shot area, i.e., that the reticle be aligned exactly with the wafer. At present, a dominant method in the stepper is an enhanced global alignment (EGA) method disclosed in U.S. Pat. No. 4,780,617 and U.S. Pat. No. 4,833,621.
Now, a plurality of shot areas on the wafer are regularly arrayed based on predetermined array coordinates. Even when stepping the wafer on the basis of design array coordinate values (array of shot areas) of the plurality of shot areas on the wafer, however, each shot area is not necessarily precisely aligned due to the following factors:
(1) a residual rotational error .theta. of the wafer; PA1 (2) a degree-of-orthogonality error w of a stage coordinate system (or the array of shot areas); PA1 (3) wafer linear expansions (scaling) Rx, Ry; and PA1 (4) offsets (parallel movements) Ox, Oy of the wafer (a central position).
Herein, the on-wafer array coordinates on the basis of four error quantities (six parameters) can be described by a linear transformation formula. Then, according to the EGA method, a linear transformation model for transforming a coordinate system (x, y) into a stage coordinate system (X, Y) is expressed as shown in the following formula by use of the six transform parameters a-f: ##EQU1##
The six transform parameters a-f in the formula (1) can be obtained by use of, e.g., the least squares method. That is, each of n-pieces of shot areas (hereinafter called sample shot areas) selected from a plurality of shot areas on the wafer is aligned to a predetermined fiducial position in accordance with array coordinates (x1, y1), . . . , (xn, yn) in terms of design. Measured subsequently is each of coordinate values (XM1, YM1), . . . , (XMn, YMn), on the stage coordinate system, of each of the n-pieces of sample shot areas.
Regarded herein as alignment errors are differences (.DELTA.x, .DELTA.y) between the design array coordinates (xi, yi) (i=1, 2, . . . , n) obtained by substituting the sample shot areas into the linear transformation model of the formula (1) and the above measured values (XMi, YMi). At this time, the alignment error .DELTA.x is expressed by .SIGMA.(Xi-XMi).sup.2, while the alignment error .DELTA.y is expressed by .SIGMA.(Yi-YMi).
Next, the alignment errors .DELTA.x, .DELTA.y are partially differentiated in sequence by the six transform parameters a-f, and there is established such an equation as making its value 0. These six simultaneous equations are solved, thereby obtaining the six transform parameters. Then, the array coordinates of all the shot areas on the wafer are calculated from the formula (1) by use of the thus obtained transform parameters a-f. When the wafer is located according to the thus calculated array coordinates, all the shot areas can be accurately aligned. Note that e.g., second- or higher-order equations are, as is proposed in Ser. No. 011,697 (Feb. 1, 1993) now abandoned, employed if a good approximate accuracy is not obtained in the above linear transformation model (the formula (1)).
By the way, the linear approximation is effected according to the EGA method, and hence, if the wafer has a non-linear distortion, there exists a drawback to reduce the alignment accuracy. Under such circumstances, Ser. No. 005,146 (Jan. 15, 1993) now abandoned proposes a weighted EGA method for obtaining the transform parameters a-f in the formula (1) by using the least squares method. This method involves a step of expressing the alignment errors .DELTA.x, .DELTA.y such as .SIGMA.Wi (Xi-XMi).sup.2, .SIGMA.Wi (Yi-YMi).sup.2 by employing the weight Wi corresponding to a distance between one shot area on the wafer and each of the n-pieces of sample shot areas.
According to the weighted EGA method, the weight Wi increases with respect to the sample shot area closer to the shot area. The reason for this is that the sample shot area in closer proximity to the shot area, it is considered, undergoes a smaller influence of the non-linear distortion. However, it may happen that a non-linear distortion quantity does not depend on the distance between the shot area and the sample shot area. For example, if a local non-linear distortion exists, the distortion quantity increases without depending on the above distance in some cases. For this reason, even when adopting the weighted EGA method, there is a drawback in which the alignment errors due to the non-linear distortion can not be reduced.
According further to the weighted EGA method, the sample shot areas effective in use for calculating the coordinate positions of the shot areas exist in a circle having a predetermined radius about the shot area concerned. A range (area) where these effective sample shot areas exist is termed a [zone]. Accordingly, an outline of the zone assumes a substantially circular shape with respect to the shot areas existing at the center of the wafer. In contrast with this, when the shot areas are disposed along the periphery of the wafer, the zone takes a partially-chipped circle, resulting in a reduction in terms of the number of effective sample shot areas. Consequently, data about the distortion can not be accurately obtained in the peripheral portion of the wafer. An averaging effect by the plurality of sample shot areas can not be expected, and, hence, there arises a disadvantage of worsening an accuracy of calculating the coordinate positions. For avoiding this, if a large number of sample shot areas are disposed along the periphery of the wafer, the distortion data become excessive in the peripheral portion thereof. The calculation accuracy of the coordinate positions relatively decreases at the central portion of the wafer where a small number of sample shot areas exist. Further, if a total number of sample shot areas increases, there is produced such a drawback that a throughput decreases because of taking much time for the coordinate measurement.
Further, an alignment sensor for detecting alignment marks for the sample shot areas in order to measure the coordinate positions thereof has a scatter in terms of a measurement reproducibility (a measurement accuracy). For instance, when measuring the coordinate positions of the sample shot areas by employing the alignment sensor exhibiting a bad measurement reproducibility, the measured coordinate position may deviate largely from a true value. Accordingly, even when adopting the weighted EGA method, and if the above-mentioned coordinate positions exhibiting a low reliability are used, there is caused a drawback of decreasing the alignment accuracy. This will be specifically explained with reference to FIGS. 22 and 23.
Referring to FIGS. 22 and 23, the horizontal axis indicates X-coordinates of the stage coordinate system, while the vertical axis of ordinate indicates a X-directional deviation quantity .delta.X of a true coordinate position with respect to a design coordinate position (when linear/non-linear distortions and scaling are not caused) in the shot area.
Turning to FIG. 22, a curve 170 represents the X-directional true deviation quantity .delta.X of each shot area, and points 171A-171I shown by white or black circles respectively indicate X-directional deviation quantities of nine sample shot areas which are measured by using the alignment sensor. Further, as shown by error bars added to the respective points 171A-171I, each measured value of the alignment sensor has a scatter on the order of .+-..sigma..sub.1 (a standard deviation .sigma. or 3.sigma.). When calculating a coordinate position of the sample shot area corresponding to, e.g., the point 171G by the weighted EGA method, the point 172G on an approximate straight line 172 obtained by giving a large weight to each of the coordinate positions of the sample shot areas corresponding to the points 171F, 71G, 171H in the vicinity thereof turns out an X-directional deviation quantity of the coordinate position in terms of calculation. At this time, as illustrated in FIG. 22, if the scatter .sigma..sub.1 of the measured result is small, viz., if a good measurement reproducibility is exhibited, a difference between the calculated coordinate position and the true coordinate position on the curve 170 is small. Then, it follows that the alignment can be performed with a high accuracy.
On the other hand, FIG. 23 shows a case where a scatter .+-..sigma..sub.2 of the measured result is larger (a bad measurement reproducibility) than in FIG. 22. Referring to FIG. 23, a curve 173 indicates an X-directional true deviation quantity .delta.X of each shot area. Points 174A-174I marked with white or black circles represent X-directional deviation quantities of the nine sample shot areas which are measured by use of the alignment sensor. When calculating the coordinate position of the sample shot area corresponding to, e.g., the point 174G by the weighted EGA method, the point 175G on an approximate straight line 175 obtained by giving a larger weight to each coordinate position of the sample shot areas corresponding to the points 174F, 174G, 174H in the vicinity thereof turns out an X-directional deviation quantity of the calculated coordinate position. As shown in FIG. 23, if a scatter .sigma..sub.2 of the measured result is large, however, there increases a difference between the calculated coordinate position and the true coordinate position on the curve 173. That is, if the measurement reproducibility is bad, the coordinate position calculated based on the weighted EGA method deviates by a measurement error, resulting in such a drawback that the alignment accuracy is not improved so much.